Musical acoustics or
music acoustics is the branch of
acousticsAcoustics is the interdisciplinary science that deals with the study of sound, ultrasound and infrasound . A scientist who works in the field of acoustics is an acoustician. The application of acoustics in technology is called acoustical engineering...
concerned with researching and describing the
physicsPhysics is a natural science; it is the study of matter and its motion through spacetime and all that derives from these, such as energy and force...
of
musicMusic is an art form whose medium is sound. Common elements of music are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...
— how sounds employed as music work. Examples of areas of study are the function of musical instruments, the
human voiceThe human voice consists of sound made by a human being using the vocal folds for talking, singing, laughing, crying, screaming, etc. Human voice is specifically that part of human sound production in which the vocal folds are the primary sound source...
(the physics of
speechInterpersonal communication is defined by communication scholars in numerous ways, usually describing participants who are dependent upon one another and have a shared history...
and
singingSinging is the act of producing musical sounds with the voice, and augments regular speech by the use of both tonality and rhythm. A person who sings is called a singer or vocalist...
), computer analysis of
melodyA melody , also tune, voice, or line, is a linear succession of musical tones which is perceived as a single entity...
.
Methods and fields of study
- Frequency Range of Music
In music, the terms range, designated range, sounding range and written range have specific meanings.The range of a musical instrument is the distance from the lowest to the highest pitch it can play. For a singing voice, this is known as vocal range. The range of a musical part is the distance...
- Frequency analysis
In cryptanalysis, frequency analysis is the study of the frequency of letters or groups of letters in a ciphertext. The method is used as an aid to breaking classical ciphers....
- Computer analysis
Musical analysis can be defined as an attempt to answer the question how does this music work?. The method employed to answer this question, and indeed exactly what is meant by the question, differs from analyst to analyst, and according to the purpose of the analysis. According to Ian Bent ,...
of musical structure
- Synthesis
In music technology, sound synthesis is the process of generating sound from analogue and digital electronic equipment, often for musical, artistic or entertainment purposes. In particular, it refers to the process of generating, combining or mixing sounds from a set of fundamental building blocks...
of musical sounds
- Music cognition
Music cognition is an interdisciplinary approach to understanding the mental processes that support musical behaviors, including perception, comprehension, memory, attention, and performance...
, based on physics (also known as psychoacousticsPsychoacoustics is the study of subjective human perception of sounds. Alternatively it can be described as the study of the psychological correlates of the physical parameters of acoustics.- Background :...
)
Physical aspects
Whenever two different pitches are played at the same time, their sound waves interact with each other — the highs and lows in the air pressure reinforce each other to produce a different sound wave. As a result, any given sound wave which is more complicated than a sine wave can be modelled by many different sine waves of the appropriate frequencies and amplitudes (a
frequency spectrumFamiliar concepts associated with a frequency are colors, musical notes, radio/TV channels, and even the regular rotation of the earth. A source of light can have many colors mixed together and in different amounts . A rainbow, or prism, sends the different frequencies in different directions,...
). In
humanHumans are bipedal primates belonging to the species Homo sapiens in Hominidae, the great ape family. They are the only surviving member of the genus Homo. Humans have a highly developed brain, capable of abstract reasoning, language, introspection, and problem solving...
s the
hearingHearing is one of the traditional five senses. It is the ability to perceive sound by detecting vibrations via an organ such as the ear...
apparatus (composed of the
earThe ear is the organ that detects sound. The vertebrate ear shows a common biology from fish to humans, with variations in structure according to order and species. It not only acts as a receiver for sound, but plays a major role in the sense of balance and body position...
s and
brainThe brain is the center of the nervous system in all vertebrate, and most invertebrate, animals. Some primitive animals such as jellyfish and starfish have a decentralized nervous system without a brain, while sponges lack any nervous system at all...
) can usually isolate these tones and hear them distinctly. When two or more tones are played at once, a variation of air pressure at the ear "contains" the pitches of each, and the ear and/or brain isolate and decode them into distinct tones.
When the original sound sources are perfectly periodic, the
noteIn music, the term note has two primary meanings:#a sign used in musical notation to represent the relative duration and pitch of a sound;#a pitched sound itself....
consists of several related sine waves (which mathematically add to each other) called the
fundamentalFundamental may refer to:* Foundation of reality.* Fundamental frequency, as in music or phonetics, often referred to as simply a "fundamental"....
and the
harmonicIn acoustics and telecommunication, a harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. For example, if the fundamental frequency is...
s,
partial* of or relating to a part rather than the whole, not general or total .* inclined to favor one party more than the other, biased. * markedly fond of someone or something, used with to. * of or relating to a part rather than the whole, not general or total (a partial solution).* inclined to favor...
s, or
overtoneAn overtone is a natural resonance of a system. Systems described by overtones are often sound systems, for example, blown pipes or plucked strings.If such a system is excited, a number of tones may be produced along with the fundamental tone...
s. The sounds have
harmonicIn acoustics and telecommunication, a harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. For example, if the fundamental frequency is...
frequency spectraFamiliar concepts associated with a frequency are colors, musical notes, radio/TV channels, and even the regular rotation of the earth. A source of light can have many colors mixed together and in different amounts . A rainbow, or prism, sends the different frequencies in different directions,...
. The lowest frequency present is the fundamental, and is the frequency at which the entire wave vibrates. The overtones vibrate faster than the fundamental, but must vibrate at integer multiples of the fundamental frequency in order for the total wave to be exactly the same each cycle. Real instruments are close to periodic, but the frequencies of the overtones are slightly imperfect, so the shape of the wave changes slightly over time.
Subjective aspects
Variations in air
pressurePressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
against the
earThe ear is the organ that detects sound. The vertebrate ear shows a common biology from fish to humans, with variations in structure according to order and species. It not only acts as a receiver for sound, but plays a major role in the sense of balance and body position...
drum, and the subsequent physical and neurological processing and interpretation, give rise to the subjective experience called "
soundSound is a travelling wave which is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.- Perception of sound...
". Most sound that people recognize as "
musicMusic is an art form whose medium is sound. Common elements of music are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...
al" is dominated by
periodicPeriodicity is the quality of occurring at regular intervals or periods and can occur in different contexts:In timing devices:* A clock marks time at periodic intervals.* A metronome ticks at periodic intervals of time....
or regular vibrations rather than non-periodic ones (called a definite pitch), and we refer to the transmission mechanism as a "sound wave". In a very simple case, the sound of a
sine waveThe sine wave or sinusoid is a function that occurs often in mathematics, music, physics, signal processing, audition, electrical engineering, and many other fields...
, which is considered to be the most basic model of a sound waveform, causes the air pressure to increase and decrease in a regular fashion, and is heard as a very "pure" tone. Pure tones can be produced by
tuning forkA tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs formed from a U-shaped bar of elastic metal . It resonates at a specific constant pitch when set vibrating by striking it against a surface or with an object, and emits a pure musical tone after waiting a...
s or
whistlingHuman whistling is the production of sound by means of carefully controlling a stream of air flowing through a small hole. Whistling can be achieved by creating a small opening with one's lips and then blowing air out of the hole or sucking air into the hole...
. The rate at which the air pressure varies governs is the
frequencyFrequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency....
of the tone, which is measured in oscillations per second, called
hertzThe hertz is a unit of frequency. It is defined as the number of complete cycles per second. It is the basic unit of frequency in the International System of Units , and is used worldwide in both general-purpose and scientific contexts...
. Frequency is a primary determinate of the perceived
pitchPitch represents the perceived fundamental frequency of a sound. It is one of the three major auditory attributes of sounds along with loudness and timbre. When the actual fundamental frequency can be precisely determined through physical measurement, it may differ from the perceived pitch because...
. Frequency can change with Altitude due to changes in air pressure. This is called the Adiabatic
Lapse RateThe lapse rate is defined as the rate of decrease with height for an atmospheric variable. The variable involved is temperature unless specified otherwise. The terminology arises from the word lapse in the sense of a decrease or decline; thus, the lapse rate is the rate of decrease with height and...
Frequency Range of Music
Harmonics, partials, and overtones
The fundamental is the frequency at which the entire wave vibrates. Overtones are other sinusoidal components present at frequencies above the fundamental. All of the frequency components that make up the total waveform, including the fundamental and the overtones, are called
partial* of or relating to a part rather than the whole, not general or total .* inclined to favor one party more than the other, biased. * markedly fond of someone or something, used with to. * of or relating to a part rather than the whole, not general or total (a partial solution).* inclined to favor...
s. Together they form the
harmonic seriesPitched musical instruments are often based on an approximate harmonic oscillator such as a string or a column of air, which oscillates at numerous frequencies simultaneously. At these resonant frequencies, waves travel in both directions along the string or air column, reinforcing and canceling...
.
Overtones which are perfect integer multiples of the fundamental are called
harmonicIn acoustics and telecommunication, a harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. For example, if the fundamental frequency is...
s. When an overtone is near to being harmonic, but not exact, it is sometimes called a harmonic partial, although they are often referred to simply as harmonics. Sometimes overtones are created that are not anywhere near a harmonic, and are just called partials or inharmonic overtones.
The fundamental frequency is considered the
first harmonic and the
first partial. The numbering of the partials and harmonics is then usually the same; the second partial is the second harmonic, etc. But if there are inharmonic partials, the numbering no longer coincides. Overtones are numbered as they appear
above the fundamental. So strictly speaking, the
first overtone is the
second partial (and usually the
second harmonic). As this can result in confusion, only harmonics are usually referred to by their numbers, and overtones and partials are described by their relationships to those harmonics.
Harmonics and non-linearities
When a periodic wave is composed of a fundamental and only odd harmonics (f, 3f, 5f, 7f, ...), the summed wave is
half-wave symmetric; it can be inverted and phase shifted and be exactly the same. If the wave has any even harmonics (0f, 2f, 4f, 6f, ...), it will be asymmetrical; the top half will not be a mirror image of the bottom.
The opposite is also true. A system which changes the shape of the wave (beyond simple scaling or shifting) creates additional harmonics (harmonic distortion). This is called a
non-linear system. If it affects the wave symmetrically, the harmonics produced will only be odd, if asymmetrically, at least one even harmonic will be produced (and probably also odd).
Harmony
If two notes are simultaneously played, with frequency
ratioA ratio is an expression that compares quantities relative to each other. The most common examples involve two quantities, but any number of quantities can be compared. Ratios are represented mathematically by separating each quantity with a colon – for example, the ratio 2:3, which is read as the...
s that are simple fractions (e.g. 2/1, 3/2 or 5/4), then the composite wave will still be periodic with a short period, and the combination will sound
consonantConsonance is a stylistic device, most commonly used in poetry and songs, characterized by the repetition of the same consonant two or more times in short succession, as in "pitter patter" or in "all mammals named Sam are clammy".Consonance should not be confused with assonance, which is the...
. For instance, a note vibrating at 200 Hz and a note vibrating at 300 Hz (a
perfect fifthThe perfect fifth is the musical interval between a note and the note seven semitones above it on the musical scale. For example, the note G lies a perfect fifth above C; D is a perfect fifth above G, C is a perfect fifth above F...
, or 3/2 ratio, above 200 Hz) will add together to make a wave that repeats at 100 Hz: every 1/100 of a second, the 300 Hz wave will repeat thrice and the 200 Hz wave will repeat twice. Note that the total wave repeats at 100 Hz, but there is not actually a 100 Hz sinusoidal component present.
Additionally, the two notes will have many of the same partials. For instance, a note with a fundamental frequency of 200 Hz will have harmonics at:
400, 600, 800, 1000, 1200, …
A note with fundamental frequency of 300 Hz will have harmonics at:
600, 900, 1200, 1500, …
The two notes have the harmonics 600 and 1200 in common, and more will coincide further up the series.
The combination of composite waves with short fundamental frequencies and shared or closely related partials is what causes the sensation of
harmonyIn music, harmony is the use of simultaneous pitches, or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic...
.
When two frequencies are near to a simple fraction, but not exact, the composite wave cycles slowly enough to hear the cancellation of the waves as a steady pulsing instead of a tone. This is called
beatingIn acoustics, a beat is an interference between two sounds of slightly different frequencies, perceived as periodic variations in volume whose rate is the difference between the two frequencies....
, and is considered to be unpleasant, or
dissonantIn music, a consonance is a harmony, chord, or interval considered stable, as opposed to a dissonance — considered unstable...
.
The frequency of beating is calculated as the difference between the frequencies of the two notes. For the example above, |200 Hz - 300 Hz| = 100 Hz. As another example, a combination of 3425 Hz and 3426 Hz would beat once per second (|3425 Hz - 3426 Hz| = 1 Hz). This follows from
modulationModulation is the process of varying one waveform in relation to another waveform. In telecommunications, modulation is used to convey a message, or a musician may modulate the tone from a musical instrument by varying its volume, timing and pitch. Often a high-frequency sinusoid waveform is used...
theory.
The difference between consonance and dissonance is not clearly defined, but the higher the beat frequency, the more likely the interval to be dissonant.
HelmholtzHermann Ludwig Ferdinand von Helmholtz was a German physician and physicist who made significant contributions to several widely varied areas of modern science...
proposed that maximum dissonance would arise between two pure tones when the beat rate is roughly 35 Hz.
http://www.music-cog.ohio-state.edu/Music829B/roughness.html
Scales
The material of a musical composition is usually taken from a collection of pitches known as a
scaleIn music, a scale is a group of musical notes collected in ascending and descending order, that provides material for or is used to conveniently represent part or all of a musical work including melody and/or harmony...
. Because most people cannot adequately determine
absoluteAbsolute pitch , widely referred to as perfect pitch, is the ability of a person to identify or recreate a musical note without the benefit of an external reference.-Definition:...
frequencies, the identity of a scale lies in the ratios of frequencies between its tones (known as
intervalsIn music theory, the term interval describes the relationship between the pitches of two notes.Intervals may be described as:* vertical if the two notes sound simultaneously* linear , if the notes sound successively....
).
The
diatonic scaleIn music theory, a diatonic scale is a seven note musical scale comprising five whole steps and two half steps, in which the half steps are maximally separated...
appears in writing throughout history, consisting of seven tones in each
octaveIn music, an octave , is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon which has been referred to as the "basic miracle of music," the use of which is "common in most musical systems." It may be derived from the...
. In
just intonationIn music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of whole numbers. Any interval tuned in this way is called a just interval; in other words, the two notes are members of the same harmonic series....
the diatonic scale may be easily constructed using the three simplest intervals within the octave, the
perfect fifthThe perfect fifth is the musical interval between a note and the note seven semitones above it on the musical scale. For example, the note G lies a perfect fifth above C; D is a perfect fifth above G, C is a perfect fifth above F...
(3/2),
perfect fourthThe perfect fourth is a musical interval which spans four scale degrees. It consists of the note and the note five semitones above it on the musical scale. For example, the interval between a C and the next F above it is a perfect fourth; similarly the interval between a G and the next C above...
(4/3), and the
major thirdA major third is one of two commonly occurring musical intervals that span three diatonic scale degrees, the other being the minor third. It is denoted 'major' because it is the larger of the two: the major third is a leap of four semitones, the minor third three. The major third is abbreviated...
(5/4). As forms of the fifth and third are naturally present in the overtone series of harmonic resonators, this is a very simple process.
The following table shows the ratios between the frequencies of all the notes of the just
major scaleIn music theory, the major scale or Ionian scale is one of the diatonic scales. It is made up of seven distinct notes, plus an eighth which duplicates the first an octave higher. In solfege these notes correspond to the syllables "Do, Re, Mi, Fa, Sol, La, Ti, "...
and the fixed frequency of the first note of the scale.
| C | D | E | F | G | A | B | C |
|---|
| 1 |
9/8 |
5/4 |
4/3 |
3/2 |
5/3 |
15/8 |
2 |
There are other scales available through just intonation, for example the
minor scaleA minor scale in music theory is a diatonic scale with a third scale degree at an interval of a minor third above the tonic. While this definition encompasses modes with the minor third, such as Dorian mode, the term may more usually refer only to the natural minor, harmonic minor, and melodic...
. Scales which do not adhere to just intonation, and instead have their intervals adjusted to meet other needs are known as
temperamentsIn musical tuning, a temperament is a system of tuning which slightly compromises the pure intervals of just intonation in order to meet other requirements of the system....
, of which
equal temperamentEqual temperament is a musical temperament, or a system of tuning in which every pair of adjacent notes has an identical frequency ratio. In equal temperament tunings, an interval — usually the octave — is divided into a series of equal steps...
is the most used. Temperaments, though they obscure the acoustical purity of just intervals often have other desirable properties, such as a closed
circle of fifthsIn music theory, the circle of fifths shows the relationships among the twelve tones of the chromatic scale, their corresponding key signatures, and the associated major and minor keys. More specifically, it is a geometrical representation of relationships among the 12 pitch classes of the...
.
Further reading
- Seashore, Carl Emil
Carl Emil Seashore was a prominent American psychologist.-Background:Seashore was born in Mörlunda, Hultsfred Municipality, Kalmar County, Sweden to Carl Gustav and Emily Sjostrand. He emigrated with his family to the United States in 1870 and settled in Iowa. The name “Seashore” is a...
, "The Psychology of Music", McGraw-Hill, 1938. ISBN 0486218511 (Dover PublicationsDover Publications is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche. It publishes primarily reissues, books no longer published by their original publishers — often, but not always, books in the public domain...
reprint)
See also
- Sound
Sound is a travelling wave which is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.- Perception of sound...
- Acoustics
Acoustics is the interdisciplinary science that deals with the study of sound, ultrasound and infrasound . A scientist who works in the field of acoustics is an acoustician. The application of acoustics in technology is called acoustical engineering...
- Harmony
In music, harmony is the use of simultaneous pitches, or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic...
- Mathematics of musical scales
- Vibrating string
A vibration in a string is a wave. Usually a vibrating string produces a sound whose frequency in most cases is constant. Therefore, since frequency characterizes the pitch, the sound produced is a constant note....
- Open tube
In the field of acoustics, a tone is created by the periodic vibrations of air. There are several ways in music to create such vibrations. One of these is to use a tube and to blow across the end. This creates a note of a given frequency, depending on the length of the tube and the pressure of the...
- Closed tube
In the field of acoustics, a tone is created by the periodic vibrations of air applied to a resonator. There are several ways in music to create such vibrations. One of these is to use a closed tube and to blow across the end. This creates a Bernoulli, or "siphon", effect just below the open end or...
- String resonance (music)
String resonance occurs on string instruments. Strings or parts of strings may resonate at their fundamental or overtone frequencies when other strings are sounded...
- 3rd Bridge
The 3rd bridge is an extended playing technique used on some string instruments , which allows a musician to produce distinctive timbres and overtones which are unavailable on a conventional string instrument with two bridges....
(harmonic resonance based on equal string divisions)
External links